/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:		arm_var_q31.c
*
* Description:	Variance of an array of Q31 type.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated.
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupStats
 */

/**
 * @addtogroup variance
 * @{
 */

/**
 * @brief Variance of the elements of a Q31 vector.
 * @param[in]       *pSrc points to the input vector
 * @param[in]       blockSize length of the input vector
 * @param[out]      *pResult variance value returned here
 * @return none.
 *
 * @details
 * <b>Scaling and Overflow Behavior:</b>
 *
 *\par
 * The function is implemented using an internal 64-bit accumulator.
 * The input is represented in 1.31 format, and intermediate multiplication
 * yields a 2.62 format.
 * The accumulator maintains full precision of the intermediate multiplication results,
 * but provides only a single guard bit.
 * There is no saturation on intermediate additions.
 * If the accumulator overflows it wraps around and distorts the result.
 * In order to avoid overflows completely the input signal must be scaled down by
 * log2(blockSize) bits, as a total of blockSize additions are performed internally.
 * Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.
 *
 */


void arm_var_q31(
    q31_t* pSrc,
    uint32_t blockSize,
    q63_t* pResult)
{
	q63_t sum = 0, sumSquare = 0;                  /* Accumulator */
	q31_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
	q31_t mean;                                    /* mean */
	q31_t in;                                      /* input value */
	q31_t t;                                       /* Temporary variable */
	uint32_t blkCnt;                               /* loop counter */

#ifndef ARM_MATH_CM0

	/* Run the below code for Cortex-M4 and Cortex-M3 */
	q63_t sumSquare1 = 0;                          /* Accumulator */
	q31_t in1, in2, in3, in4;                      /* Temporary input variables */

	/*loop Unrolling */
	blkCnt = blockSize >> 2u;

	/* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
	 ** a second loop below computes the remaining 1 to 3 samples. */
	while(blkCnt > 0u) {
		/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
		/* Compute Sum of squares of the input samples
		 * and then store the result in a temporary variable, sum. */
		/* read input samples from source buffer */
		in1 = pSrc[0];
		in2 = pSrc[1];

		/* calculate sum of inputs */
		sum += in1;
		/* calculate sum of squares */
		sumSquare += ((q63_t)(in1) * (in1));
		in3 = pSrc[2];
		sum += in2;
		sumSquare1 += ((q63_t)(in2) * (in2));
		in4 = pSrc[3];
		sum += in3;
		sumSquare += ((q63_t)(in3) * (in3));
		sum += in4;
		sumSquare1 += ((q63_t)(in4) * (in4));

		/* update input pointer to process next samples */
		pSrc += 4u;

		/* Decrement the loop counter */
		blkCnt--;
	}

	/* add two accumulators */
	sumSquare = sumSquare + sumSquare1;

	/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
	 ** No loop unrolling is used. */
	blkCnt = blockSize % 0x4u;

#else

	/* Run the below code for Cortex-M0 */
	blkCnt = blockSize;

#endif /* #ifndef ARM_MATH_CM0 */

	while(blkCnt > 0u) {
		/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
		/* Compute Sum of squares of the input samples
		 * and then store the result in a temporary variable, sum. */
		in = *pSrc++;
		sumSquare += ((q63_t)(in) * (in));
		sum += in;

		/* Decrement the loop counter */
		blkCnt--;
	}

	t = (q31_t)((1.0f / (float32_t)(blockSize - 1u)) * 1073741824.0f);

	/* Compute Mean of squares of the input samples
	 * and then store the result in a temporary variable, meanOfSquares. */
	sumSquare = (sumSquare >> 31);
	meanOfSquares = (q31_t)((sumSquare * t) >> 30);

	/* Compute mean of all input values */
	t = (q31_t)((1.0f / (blockSize * (blockSize - 1u))) * 2147483648.0f);
	mean = (q31_t)(sum);

	/* Compute square of mean */
	squareOfMean = (q31_t)(((q63_t) mean * mean) >> 31);
	squareOfMean = (q31_t)(((q63_t) squareOfMean * t) >> 31);

	/* Compute variance and then store the result to the destination */
	*pResult = (q63_t) meanOfSquares - squareOfMean;

}

/**
 * @} end of variance group
 */
